Dark Spatial Solitary Wave Due to Cascaded x^（2） Nonlinearity

The formation of the dark spatial solitary wave in cascaded second harmonic generation processes is numerically studied based on the nonlinear-coupled equations. It is shown that the solitary wave exists when the effective three-order nonlinearity induced by cascaded second-order nonlinearity is negative.     

Spatial temporal wave mixing for space time conversion

A nonlinear optical processor that is capable of true real-time conversion of spatial-domain images to ultrafast time-domain optical waveforms is presented. The method is based on four-wave mixing between the optical waves of spectrally decomposed ultrashort pulses and spatially Fourier-transformed quasi-monochromatic images. To achieve efficient wave mixing at a femtosecond rate we utilize a cascaded second-order nonlinearity arrangement in a beta-barium borate crystal with type II phase matching. We use this ultrafast technique to experimentally generate several complex-amplitude temporal waveforms, with efficiency as high as 10%, by virtue of the cascaded nonlinearity arrangement.     

Solitary wave solutions for nonlinear Schrödinger equation with non-polynomial nonlinearity

A new kind of non-polynomial nonlinearity is introduced in the nonlinear Schrödinger equation (NLSE) and the conditions are determined for which it admits solitary wave solutions. The study is done for two cases: one in which the nonlinear interaction is of the non-polynomial form and second in which cubic nonlinearity is also included along with the radical nonlinearity. Dark and bright solitary waves solutions are obtained in the respective cases. Further, later case is extended to conditions for which corresponding equation reduces to driven quadratic-cubic NLSE possessing cnoidal solutions with plane wave phase, which reduces to bright soliton for a certain parameter.     

Soliton and shock wave solutions to the Degasperis–Procesi equation with power law nonlinearity

This paper obtains the solitary wave as well as the shock wave solutions of the Degasperis–Procesi equation. Both regular nonlinearity as well as power law nonlinearity are considered. The constraint relations are identified in the process of obtaining the nonlinear wave solutions.     

Modulational instability of relativistic ion-acoustic waves in aplasma with trapped electrons

The association between the modified Korteweg-de Vries solitary wave and the modulationally unstable envelope solitary wave in a weakly relativistic unmagnetized plasma with trapped electrons is discussed. The effect of trapped electrons modifies the nonlinearity of the nonlinear Schrodinger equation and gives rise to the propagation of the modulationally unstable ion-acoustic solitary wave. The amplitude of the envelope solitary wave increases while the number of trapped electrons decreases. The velocity of the solitary wave decreases with increasing ionic temperature and increasing particle velocities. The ion oscillation mode, which satisfies the nonlinear dispersion relation, is also derived. The theory is applied to explain space observations of the solar energetic flows in interplanetary space and of the energetic particle events in the Earth's magnetosphere     

Topological and Non-topological Solitons for?the?Generalized Zakharov-Kuznetsov Modified Equal Width Equation

This paper obtains the topological and non-topological solitary wave solution of the generalized Zakharov-Kuznetsov modified equal width equation. The solitary wave ansatz method is used to carry out the integration of this equation. A couple of conserved quantities are calculated for the non-topological solitons. The domain restriction is identified for the power law nonlinearity parameter.     

Random generation of coherent solitary waves from incoherent waves

The random generation of coherent solitary waves from incoherent waves in a medium with an instantaneous nonlinearity has been observed. One excites a propagating incoherent spin wave packet in a magnetic film strip and observes the random appearance of solitary wave pulses. These pulses are as coherent as traditional solitary waves, but with random timing and a random peak amplitude.     

饱和型半导体掺杂玻璃光纤中的明暗孤子行波解

给出了饱和型半导体掺杂玻璃光纤传输方程的一般孤子行波解,讨论了在各种参数选取下解的性质以及明、暗孤波形成的条件,其中引入了通过极限零点及非极限零点来判断孤波类型的方法。 关键词：     

Polariton effect in nonlinear pulse propagation

The joint influence of the polariton effect and Kerr-like nonlinearity on the propagation of optical pulses is studied. The existence of different families of envelope solitary wave solutions in the vicinity of the polariton gap is shown. The properties of solutions depend strongly on the carrier wave frequency. In particular, solitary waves inside and outside the polariton gap exhibit different velocity and amplitude dependences on their duration.     

Exact solutions and localized excitations of a （3＋ 1）-dimensional Gross-Pitaevskii system

Periodic wave solutions and solitary wave solutions to a generalized (3+1)-dimensional Gross-Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homogeneous balance principle and a mapping approach. These exact solutions exist under certain conditions via imposing suitable constraints on the functions describing dispersion, nonlinearity, and potential. The dynamics of the derived solutions can be manipulated by prescribing specific time-modulated dispersions, nonlinearities, and potentials. The results show that the periodic waves and solitary waves with novel behaviors are similar to the similaritons reported in other nonlinear systems.     

Exact solutions and localized excitations of (3+1)-dimensional Gross—Pitaevskii system

Periodic wave solutions and solitary wave solutions to a generalized (3+1)-dimensional Gross--Pitaevskii equation with time-modulated dispersion, nonlinearity, and potential are derived in terms of an improved homogeneous balance principle and a mapping approach. These exact solutions exist under certain conditions via imposing suitable constraints on the functions describing dispersion, nonlinearity, and potential. The dynamics of the derived solutions can be manipulated by prescribing specific time-modulated dispersions, nonlinearities, and potentials. The results show that the periodic waves and solitary waves with novel behaviors are similar to similaritons reported in other nonlinear systems.     

Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity

In this Letter, we investigate the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.     

Long wave-short wave resonance in nonlinear negative refractive index media

We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.     

Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients

Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with time-dependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic, double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.     

Nonlinear directional coupler in periodically poled lithium niobate

Nonlinear wave propagation was investigated experimentally in coupled waveguides by means of the cascaded nonlinearity in quasi-phase-matched second-harmonic generation. With a specially designed wave-vector-mismatch distribution along the propagation axis, cascading was optimized for low fundamental depletion. High-contrast, ultrafast all-optical switching with switching powers of tens of watts was observed.     

Evolution of Dark Spatial Soliton in Quasi-phase-matched Quadratic Media

We theoretically investigate the evolvement of dark spatial soliton with cascading quadratic nonlinearity in quasi-phase-matched second harmonic generation. It is shown that the dark solitary wave can propagate stably when background intensity is large enough, in which diffraction of beam can be balanced by the cascading quadratic nonlinearity. We also analyze the influence of phase-mismatch on the stability of dark soliton propagation.     

Optical Solitons with Time-Dependent Dispersion, Nonlinearity and Attenuation in a Kerr-Law Media

This paper obtains the 1-soliton solution of the nonlinear Schr?dinger’s equation with Kerr law nonlinearity and time-dependent dispersion, nonlinearity and attenuation. The solitary wave ansatze is used to obtain this solution. The constraint relation between these time-dependent coefficients is also obtained for the solitons to exist. The variation of the soliton velocity also falls out by this method.     

Propagation dynamics on the Fermi-Pasta-Ulam lattices

The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate nonlinearity, the initially excited pulse may propagate coherently along the lattice for a long time in a solitary wave manner accompanied by phonon tails. The lifetime of the long-transient propagation state exhibits a sensitivity to the nonlinear parameter. The solitary wave decays exponentially during the final loss of stability, and the decay rate varying with the nonlinear parameter exhibits two different scaling laws. This decay is found to be related to the largest Lyapunov exponent of the corresponding Hamiltonian system, which manifests a transition from weak to strong chaos. The mean-free-path of the solitary waves is estimated in the strong chaos regime, which may be helpful to understand the origin of anomalous conductivity in the Fermi-Pasta-Ulam lattice.     

用推广的李群约化法求解非线性薛定谔方程

用推广的经典李群约化法，得到了色散系数、非线性系数、补偿（或损失）系数为时、空变量函数时的非线性薛定谔方程的精确解.深入研究了非线性薛定谔模型的一般孤波解与线性调频孤波解在光纤通讯与光纤放大器中的潜在应用. 关键词： 李群约化 非线性薛定谔方程 光纤通讯     

Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients

A broad class of exact self-similar solutions to the nonlinear Schr?dinger equation (NLSE) with distributed dispersion, nonlinearity, and gain or loss has been found. Appropriate solitary wave solutions applying to propagation in optical fibers and optical fiber amplifiers with these distributed parameters have also been studied. These solutions exist for physically realistic dispersion and nonlinearity profiles in a fiber with anomalous group velocity dispersion. They correspond either to compressing or spreading solitary pulses which maintain a linear chirp or to chirped oscillatory solutions. The stability of these solutions has been confirmed by numerical simulations of the NLSE.